Melody

Rainbow Panda I DID spend quite a bit of time explaining this to you.

Ok, I see you did not understand.   That is ok.  I am sorry I was not around to elaborate for you. 

My only thought is that you should have explained this briefly here and  included a link to the original post but that is not a huge deal.

I hope you understand now :)

Original post:

Hi Rainbow Panda,

1a)      \(\displaystyle\lim_{x\rightarrow \infty} f(x) = \infty\\ \\~\\ \displaystyle\lim_{x\rightarrow -\infty} f(x) =- \infty\\\)

 You can do 2a yourself

 b)

The x axis is the axis of symmetry of all even graphs   That is   f(-x) = f(x)

Odd functions  have 180 degree rotational symmetry about (0,0)    That mean    f(-x) = -f(x)

Are either of these even or odd?

c)  If it finishes in the top right corner where y is positive then the leading coefficient is  +

If it finishes in the bottom right corner where y is negative then the leading coefficient is  -

The leading coefficient is the number in front of the highest power of x.

So now you should be able to answer the rest yourself ;)  

Thanks Very much Heureka :)

Yes you are right about the wording. 

The original wording is clumsy but I made it much worse and I expect my logic is no longer correct.

I will think about it more if i get around to it. :/

Ten people are sitting in a row, and each is thinking of a negative integer no smaller than -15. Each person subtracts, from his own number, from the number of the person sitting to his right (the rightmost person does nothing). Because he has nothing else to do, the rightmost person observes that all the differences were positive. Let x be the greatest integer owned by one of the 10 people at the beginning. What is the minimum possible value of x?

I added a word because it was missing.

The means that the numbers must increase from left to right.

The left most cannot be smaller than -15 so the right most cannot be smaller than -6  

The minumum possible value of x is -6

Please do not delete questions.  It is very rude because someone could have been in the process of answering it.

It is ok to write a new post saying  "Thanks for looking at my question but don't worry because I have worked it out myself"

Or whatever you want to say.

I have never learnt to do modulus arithemtic formally (I'm self taught) so it would be good if someone checked this answer.

Thanks :)

What is the largest negative x integer  satisfying    \( 24x \equiv 15 \pmod{1199}~? \)

15 (mod1199)  is equivalent to  15-1199- 1199k = -1184 - 1199k   (mod1199)

24x =  -1184 - 1199k

1199k+24x = -1184

there does not appear to be any common factors

Look for a solution to   1199k+24x=-1

1199=50*24-1

so

1199(1)+24(-50)=-1

and

1199(1184   )+24(-50*1184   )=-1184

the general solution is

1199(1184 -24a  )+24(-50*1184 + 1199a   )=-1184      where a is an integer

so I think I want   

\(-50*1184+1199a<0\\ 1199a<58200\\ a<49.37\\ \text{but a is an integer so the biggest a is 49}\)

\(1199(1184-24*49) +24(-50*1184+1199*49)=-1184\\ 1184(8)+24(-449)=-1184\)

\( 24*-449 \equiv 15 \pmod{1199} \)

So I think that the negative integer with the smallest absolute value (that is the biggest one) is 

\(x= -449\)